Loading...

System of Equations Solver

Solve a system of two linear equations with two unknowns. Enter coefficients for ax+by=c and dx+ey=f.

Math

Share

a (1st eq, x)

b (1st eq, y)

c (1st eq, constant)

d (2nd eq, x)

e (2nd eq, y)

f (2nd eq, constant)

Formula

Solve a system of two linear equations in two unknowns using Cramer's rule. Enter equations in the form ax+by=c and dx+ey=f.

ax+by=c, dx+ey=f → solve for x,y

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter coefficients a, b, c for the first equation ax+by=c.
2Enter coefficients d, e, f for the second equation dx+ey=f.
3Click Calculate to solve for x and y.

Examples

Solve x + y = 5, 2x - y = 0

1.Enter eq1: a=1, b=1, c=5.
2.Enter eq2: d=2, e=-1, f=0.
3.Determinant = 1(-1) - 1(2) = -3.
4.x = (5(-1) - 1(0))/-3 = 5/3, y = (1(0) - 5(2))/-3 = 10/3.

Result: x = 1.6667, y = 3.3333

Solve 3x + 2y = 7, x - y = -1

1.Enter eq1: a=3, b=2, c=7.
2.Enter eq2: d=1, e=-1, f=-1.
3.Determinant = 3(-1) - 2(1) = -5.
4.x = (7(-1) - 2(-1))/-5 = 1, y = (3(-1) - 7(1))/-5 = 2.

Result: x = 1, y = 2

Frequently Asked Questions

Cramer's rule uses determinants to solve systems of linear equations. For 2x2 systems, it gives x and y uniquely when the determinant is non-zero.

If the determinant is zero, the system either has no solutions or infinitely many solutions.

This calculator only handles two equations with two unknowns.

Just reorder your equations to the form ax+by=c. Variable names don't matter.

Yes, decimal coefficients are fully supported in all fields.

Related Calculators

Equation Solver Linear Equation Calculator Matrix Equation Solver Variable Isolation Calculator Percentage Calculator Basic Calculator

CalculateMe Team

Last updated: 2026-07-13

System of Equations Solver - Solve 2 Equations with 2 Unknowns | CalculateMe | CalculateMe